Solve Q(x+1/5)+1/4=3/4

$$Q ( x + \frac { 1 } { 5 } ) + \frac { 1 } { 4 } = \frac { 3 } { 4 }$$

Solve for Q

$$Q=\frac{5}{2\left(5x+1\right)}$$

$$x\neq -\frac{1}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply Q by x+\frac{1}{5}.

$$Qx+\frac{1}{5}Q+\frac{1}{4}=\frac{3}{4}$$

Subtract \frac{1}{4} from both sides.

$$Qx+\frac{1}{5}Q=\frac{3}{4}-\frac{1}{4}$$

Subtract \frac{1}{4} from \frac{3}{4} to get \frac{1}{2}.

$$Qx+\frac{1}{5}Q=\frac{1}{2}$$

Combine all terms containing Q.

$$\left(x+\frac{1}{5}\right)Q=\frac{1}{2}$$

Divide both sides by x+\frac{1}{5}.

$$\frac{\left(x+\frac{1}{5}\right)Q}{x+\frac{1}{5}}=\frac{\frac{1}{2}}{x+\frac{1}{5}}$$

Dividing by x+\frac{1}{5} undoes the multiplication by x+\frac{1}{5}.

$$Q=\frac{\frac{1}{2}}{x+\frac{1}{5}}$$

Divide \frac{1}{2} by x+\frac{1}{5}.

$$Q=\frac{5}{2\left(5x+1\right)}$$

Solve for x

$$x=-\frac{1}{5}+\frac{1}{2Q}$$

$$Q\neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply Q by x+\frac{1}{5}.

$$Qx+\frac{1}{5}Q+\frac{1}{4}=\frac{3}{4}$$

Subtract \frac{1}{5}Q from both sides.

$$Qx+\frac{1}{4}=\frac{3}{4}-\frac{1}{5}Q$$

Subtract \frac{1}{4} from both sides.

$$Qx=\frac{3}{4}-\frac{1}{5}Q-\frac{1}{4}$$

Subtract \frac{1}{4} from \frac{3}{4} to get \frac{1}{2}.

$$Qx=\frac{1}{2}-\frac{1}{5}Q$$

The equation is in standard form.

$$Qx=-\frac{Q}{5}+\frac{1}{2}$$

Divide both sides by Q.

$$\frac{Qx}{Q}=\frac{-\frac{Q}{5}+\frac{1}{2}}{Q}$$

Dividing by Q undoes the multiplication by Q.

$$x=\frac{-\frac{Q}{5}+\frac{1}{2}}{Q}$$

Divide \frac{1}{2}-\frac{Q}{5} by Q.

$$x=-\frac{1}{5}+\frac{1}{2Q}$$